> Second, the least significant bits that come from this generator are biased.
I don't think this is true; I'm guessing that the author borrowed this observation from one of the various other articles linked in this thread, that address the situation where we draw a 64-bit random unsigned integer and divide by `1<<64`, instead of drawing 53 bits and dividing by `1<<53`. The former does introduce a bias, but the latter doesn't (but does still limit the fraction of representable values).
I'm not sure which PRNG is used here, but some PRNGs have regularities in the lower bits.
This is e.g. the case for classical LCGs and the xoroshiro*+ family of PRNGs:
> If, however, one has to generate only 64-bit floating-point numbers (by extracting the upper 53 bits) xoshiro256+ is a slightly (≈15%) faster generator with analogous statistical properties. For general usage, one has to consider that its lowest bits have low linear complexity and will fail linearity tests (https://prng.di.unimi.it/)
> When m = 2k there is a further problem. The period of the bth bit of an LCG (where bits are numbered from the right, starting at one) is 2b , thus although the period is 2k, only the high bits are good and the lower order bits exhibit a clear repeating pattern. (https://www.pcg-random.org/pdf/hmc-cs-2014-0905.pdf)
I don't think this is true; I'm guessing that the author borrowed this observation from one of the various other articles linked in this thread, that address the situation where we draw a 64-bit random unsigned integer and divide by `1<<64`, instead of drawing 53 bits and dividing by `1<<53`. The former does introduce a bias, but the latter doesn't (but does still limit the fraction of representable values).